The coverage of the government shutdown typically goes two ways: sob stories focusing on the sympathetic casualties of government program suspensions or pat-on-the-back coverage of the private sector stepping up to easily pick up the government's slack. Saying the government is "shutdown" is a bit of an oversimplification, since 80% of it is still functioning. A guide to what services are and aren't being performed in what sectors can be found here.
Furloughed federal workers are out of work and unpaid during the shutdown.
In actuality, furloughed federal workers will be back paid for the time they were furloughed due to the government shutdown. The House has passed a measure to do so, in accordance with precedent during other government shutdowns.
Poverty programs are suspended, leaving needy mothers and children helpless. Head Start, the preschool program provided to low-income families, has stopped receiving funding. This is the only need-based program that's shut down due to the government not providing promised funding. This is unfortunate in the sense of reliability from the government, but the program itself is far from crucial in importance. I've written before about the evidence from think tanks across the spectrum that Head Start makes no discernible difference in long-term educational outcomes. WIC (food stamps) has been able to remain fully operational due to surpluses from last year and contingency funds (one wonders why this is so worrisome; what else are contingency funds for?). No other poverty programs have been affected at this point.
Food is going unexpected, resulting in health hazards. It's true that the FDA has had to furlough a majority of its inspectors. What most people don't realize, however, is that all meatpacking plants still have inspectors stationed on their lines. The dreaded salmonella outbreak due to uninspected, putrid meat flooding our supermarkets? Not likely. The furloughed inspectors are those that make surprise onsite inspections of food processing plants. Not being randomly selected to receive one for a week or two shouldn't fundamentally change the quality of our food.
There are certainly downsides to the government shutdown. Notably, spousal death benefits have not been authorized for military families. Luckily, philanthropists have volunteered to pay them for the time being. That's sort of the case in point of the whole shutdown so far.